三道门：一种基于根算子的Weil正性方法
The Three Gates: A Rooted-Operator Approach to Weil Positivity
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中文总结 AI 辅助
本文通过三道门（局部化根算子、Mellin分解与Schur几何、压缩闭包）在实数奇对数通道证明Weil正性，从Y=7出发经Schur归纳与闭包推出黎曼假设。
中文摘要 AI 辅助
我们提出了一种在实数奇对数通道中证明Weil正性的局部化根算子论证，全程保留极秩一阶项。第一道门建立了严格的胞腔/壳层符号定理，并带有严格的区间算术界。第二道门结合了Mellin单位胞腔分解、除子部分等距平方、仿射平移、全形式Cauchy--Carleman输运、相干多源短路、增广标量根以及真实度量中的Schur几何。第三道门使用压缩、闭包和受限奇Weil准则。第二道门的一个核心要点是将继承的父响应置于与算术失配和折叠标量借方相同的后旧核/公共切割原始形式中。若$P^{\rm ex}_{k,m}$是存活的继承枢轴，$a_m$是Schur极小化器的继承坐标，则$P^{\rm ex}_{k,m}a_m=\omega^{\rm ex}_{k,m}$，因此继承的源耦合贡献是该响应的负度量能量。对齐强迫被显式保留，向外取整的有限计算连同解析尾部给出$g^{M+}_k=\frac12+\log k-\frac{439}{250\log 2}\sum_m V_{k,m}-\frac52 W_k>0$对于$k\ge7$。同时公共切割定理在公共下确界之前保持父基线和横向预算分离，而折叠恒等式留下非负余数。从严格认证的端点$Y=7$出发，Schur归纳在整数端点处得到正性，零延拓在每个有限支撑半径处得到非负性，闭包连同受限奇Weil准则得到黎曼假设。简短的幻想插曲仅提供说明性地图，省略它们不会改变任何定义、引理、定理或证明。
英文摘要
We present a localized rooted-operator argument for Weil positivity in the real odd logarithmic channel, retaining the polar rank-one term throughout. The three gates are structural levels rather than a serial dependency: Gate I is an independent strict cellular/shell positivity theorem and diagnostic; Gate II carries the load-bearing operator argument; Gate III uses compression, closure, and the restricted odd Weil criterion. In Gate II, the inherited parent response is placed in the same post-old-core/common-cut primal form in which the arithmetic mismatch is charged. The audited MASTER-P2 same-block splice combines the aligned reference contribution with the actual Schur response before the target-ground coefficient is used, while the literal-slot/true-ground mismatch is paid explicitly by a leakage term. The source elimination is written as one exact common-source Schur completion on the same harmonic vector, and the endpoint fold is used only as unitary coordinate transport, so it creates no second source debit. An outward-rounded finite computation and analytic tail give a strictly positive MASTER margin for k >= 7. Starting from the rigorously certified physical coefficient-2 endpoint Y=7, Schur induction yields positivity at the integer endpoints; zero-extension gives non-negativity at every finite support radius. Closure and the restricted odd Weil criterion then give the conclusion stated in the main theorem.
